On the Modelling of Clamped Plates Loaded by a Squeeze Fluid Film: Application to Miniaturised Sensors

In order to accurately describe the processes involved in the motion of a membrane loaded by a squeeze fluid film, it is necessary to have solutions for both the membrane and the fluid film which account for their strong coupling. The dynamic solution approaches presented here include the effects of the bending stiffness of the membrane (assumed to be a clamped square plate) and the motion of the thin air film between the membrane and the backing wall, assuming realistic boundary conditions at its periphery. The mode shapes are predicted accurately for both the plate and the air film, and the approach followed includes their strong coupling. Owing to the accuracy of the method, there are applications in the characterisation of the properties of square microphones (those miniaturised on silicon chip) as shown at the end of the paper. Actually, the method would be useful for other applications which involve rectangular or square plates coupled to resistive and reactive squeeze fluid films, including or not an in-plane tension.